# Scaling Property

1. Jan 19, 2008

### dashkin111

1. The problem statement, all variables and given/known data
a system has the following property:
Its response to a sum of inputs is the sum of its responses to the inputs.

(a) Prove that the scaling property holds for any integer scaling factor
(b) Prove that the scaling property holds for any rational scaling factor

2. Relevant equations

3. The attempt at a solution
$$y_{n}(t)+...+y_{1}(t)+y_{0}(t) = x_{n}(t)+...+x_{1}(t)+x_{0}(t)$$

That's basically what it's saying, where y(t) is the response to the x(t). But I don't understand what it means by proving it, isn't it kind of trivial?

2. Jan 19, 2008

### EnumaElish

Isn't it saying y(xn + ... + x0) = y(xn) + ... + y(x0) ?

3. Jan 19, 2008

### dashkin111

Oh yeah, thanks. But still isn't it trivial to prove scaling for it?

4. Jan 19, 2008

### HallsofIvy

Staff Emeritus
Well, sometimes you are given easy problems! If you think it is trivial, go ahead and do it.